Page 80 - Fluid Power Engineering

58 Chapter Four

(less than 15 degrees) is: 2

C 2 L
C pD = (4-31)
π A r
where is the spanwise efficiency factor, A r is the aspect ratio, defined
as:

l 2
A r = (4-32)
S
l is the length of the blade, and S is the blade area. For a rectangu-
lar blade with constant chord length, A r = l/c, where c is the chord
length. As the aspect ratio increases, the pressure drag decreases.
Therefore, a long blade with short chord is preferable.

Effect of Reynolds Number on Lift and Drag Coefficients
Reynolds number of blades of wind turbines are in the range of one to
ten million. Reynolds number has a significant impact on lift and drag
coefficients.Dragcoefficientfallsandtheliftcoefficientincreasesasthe
Reynolds number is increased, as shown in Figs. 4-19 and 4-20. At low
values of α, the coefficient of drag is almost constant, and then it rises
rapidly. Reynolds number dictates the location on the aerofoil where
the flow becomes turbulent. As the Reynolds number increases, the
transition point from laminar to turbulent moves closer to the leading
edge. For low values of α, there is no separation of boundary layer, as
◦
α approaches 8 in the Fig. 4-20 example, separation occurs and the
pressure drag rapidly increases. This is the stall condition. A wind
turbine therefore avoids the stall condition during operational mode
by keeping the angle of attack low and by increasing the Reynolds
number.

FIGURE 4-19 Coeffi- C L Maximum lift
cient of lift for 1.6
different values of
Reynolds number.
Stall

Re=9 million
Re=6 million
Re=3 million

α in radians
π/12